x-5/7x=20

Solution for x-5/7x=20 equation:

x-5/7x=20

We move all terms to the left:

x-5/7x-(20)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-20*7x-5=0

Wy multiply elements

7x^2-140x-5=0

a = 7; b = -140; c = -5;
Δ = b2-4ac
Δ = -1402-4·7·(-5)
Δ = 19740
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19740}=\sqrt{4*4935}=\sqrt{4}*\sqrt{4935}=2\sqrt{4935}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4935}}{2*7}=\frac{140-2\sqrt{4935}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4935}}{2*7}=\frac{140+2\sqrt{4935}}{14}
$